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payments of PMT is
Same I/Y, P/Y, C/Y, FV
276 N 1 − ( 1 + i ) −n PV = PMT 1 PMT
i CPT PV Ans: –131.34 1 − 1.00625 −276 = PMT 0.00625 = 131.34PMT
Same I/Y, P/Y, C/Y
The PV at age 55 of this amount is
PV = FV ( 1 + i ) −n = 131.34PMT (1.00625 ) −60
= 90.37PMT
Hence, the pension-at-age-55 option has a
119.24 PMT − 90.37 PMT
×
90.37 PMT
100% = 31.9%
higher economic value Chapter 10: Ordinary Annuities: Future Value and Present Value 60 N 0 PMT
131.34 FV CPT PV Ans: –90.37 57 Exercise 10.3 (continued)
41. a. Given: For Annuity A, PMT = $100; i = 8%; n = 20
For Annuity B, PMT = $100; i = 8%; n = 40
PVB $1192.46
=
(i)
= 1.2145
PV A
$981.81
Therefore, PVB is 21.45% larger than PVA .
FVB $25,905.65
=
(ii)
= 5.6610
FV A
$4576.20
Therefore, FVB is 466.10% larger than FVA .
b. Given: For Annuity A, PMT = $100; n = 30; i = 8%
For Annuity B, PMT = $100; n = 30; i = 9%
PVB $1027.37
=
(i)
= 0.9126
PV A $1125.78
Therefore, PVB is (1 – 0.9126)× 100% = 8.74% smaller than PVA .
FVB $13,630.75
=
(ii)
= 1.2032
FV A $11,328.32
Therefore, FVB is 20.32% larger than FVA . 58 Business Mathematics in Canada, 7/e Exercise 10.4
%
1. Given: PMT = $2000, i = 72 = 3.5%, 7 I/Y P/Y 2 ENTER (making C/Y = P/Y = 2)
10 N 2000 PMT
0 FV CPT PV Ans: –16,633.211 n = 10, d = 2(5) = 10
1 − (1 + i ) − n PMT PV(5 years from now) =
i 1 − 1.035 −20
= $2000 0.035 = $16,633.211
PV(today) = FV (1 + i ) − d = $16,633.211 (1.035 ) −10
= $11,791.60 Same I/Y, P/Y, C/Y
10 N 0 PMT
16633.211 FV CPT PV Ans: −11,791.60 3. Given: PMT = $500, i = 9% = 0.75%,
12
n = 12(3.5) = 42, d = 12(2.75) = 33
1 − (1 + i ) − n PMT PV(2.75 years from now) =
i −42 1 − 1.0075
= $500 0.0075 = $17,956.856 PV(today) = FV (1 + i ) − d = $17,956.856 (1.0075 ) −33
= $14,032.77 9 I/Y P/Y 12 ENTER (making C/Y = P/Y = 12)
42 N 500 PMT
0 FV CPT PV Ans: –17,956.856 Same I/Y, P/Y, C/Y
33 N 0 PMT
17956.856 FV CPT PV Ans: −14,032.77 An investment of $14,032.77 today will support the deferred annuity payments. Chapter 10: Ordinary Annui...

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